When using ΔG=ΔG°+RT ln Q to calculate the energy yield of a reaction, does it matter if I use ΔG° calculated at 1°C or 25°C? Also, why are there two choices and when are they each applicable? Finally, I have also seen ΔG°' written (note the prime). What does this mean and how does it differ from ΔG° conceptually and numerically?

I realise that these are very basic questions, so if you want to point me towards some elementary reading material I understand.

When using ΔG=ΔG°+RT ln Q to calculate the energy yield of a reaction, does it matter if I use ΔG° calculated at 1°C or 25°C?

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Yes, it matters. If you use Delta G at 1 deg C, then you will also have to use a corresponding T and then equilibrium constant will be that for this temperature. The same way using Delta G at 25 deg Celsius yields Q for this very temperature.
The change of Q with temperature can be calculated with the van't Hoff equation:http://en.wikipedia.org/wiki/Van_'t_Hoff_equation

but what is the value of ΔG° that I should use? The value at 1ºC or 25ºC?

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Neither of the two but the value at 50 deg. Celsius.
If you have both the values at 1 and at 50 degrees, you could linearly interpolate as a first approximation.
But, as I said, it would be more exact to calculate the value of Delta G0 at 50 degs from the van't Hoff or Gibbs-Helmholtz equation, see:http://en.wikipedia.org/wiki/Gibbs-Helmholtz_equation